Question 1043151
You own a bakery which specializes in custom orders. A customer requests to have a three-tiered cake made. Requirements are as follows:

    Each tier is 15 cm high;
    The bottom tier is a cylinder with a diameter of 45 cm;
    The middle tier is a square–based prism. It must be positioned so that its corners touch the circumference of the bottom tier;
    The top tier is another cylinder inscribed in the middle tier.

You know that 250 mL of raw batter will produce 625 mL of cake. How much raw batter is required for this cake? Note: 1 mL = 1 cm3

Thanks so much :)
<pre>Volume of bottom tier (cylinder): {{{matrix(1,4, "7,593.75", pi, cu, cm)}}}
Volume of middle tier (square prism): {{{matrix(1,3, "15,187.5", cu, cm)}}}
Volume of top tier (cylinder): {{{matrix(1,4, "3,796.875", pi, cu, cm)}}}
Volume of cake: {{{matrix(1,7, "7,593.75" * pi + "15,187.5" + "3,796.875" * pi, "=", "11,390.625" * pi + "15,187.5", "=", "50,972.2", cu, cm)}}}

Since 250 mL of raw butter will produce 625 mL of cake, and with amount of raw butter needed, being B, we get: {{{250/B = 625/"50,972.2"}}}
{{{625B = 250("50,972.2")}}} ------- Cross-multiplying
B, or amount of raw butter needed = {{{highlight_green(matrix(1,4, 250("50,972.2")/625, "=", "20,388.88", mL))}}}